Counting algebraic points in expansions of o-minimal structures by a dense set

The Pila-Wilkie theorem states that if a set $X\subseteq \mathbb R^n$ is definable in an o-minimal structure $\mathcal R$ and contains `many' rational points, then it contains an infinite semialgebraic set. In this paper, we extend this theorem to an expansion $\widetilde{\mathcal R}=\langle \mathcal R, P\rangle$ of $\mathcal R$ by a dense set $P$, which is either an elementary substructure of $\mathcal R$, or it is independent, as follows. If $X$ is definable in $\widetilde{\mathcal R}$ and contains many rational points, then it is dense in an infinite semialgebraic set. Moreover, it contains an infinite set which is $\emptyset$-definable in $\langle \overline{\mathbb R}, P\rangle$, where $\overline {\mathbb R}$ is the real field

Why Max-min Fairness Is Not Suitable For Multi-Hop Wireless Networks

We consider the issue of which criteria to use when evaluating the design of a wireless multihop network. It is known, and we illustrate in this paper, that maximizing the total capacity, or transport capacity, leads to gross imbalance and is not suitable. An alternative, which is often used in networking, is to consider the max-min fair allocation of rates, or of transport rates per node. We apply max-min fairness to the class of wireless, multi-hop networks for which the rate of a wireless link is an increasing functions of signal-to-noise ratio. This class includes CDMA and UWB. We show that, for a network in this class, the max-min fair allocation of bit or transport rates always gives the same rate to all flows. We show on one example that such an allocation is highly undesirable when the network is asymmetric. Another form of fairness, utility fairness, does not appear to have the same problem

Optimal Power Control, Scheduling and Routing in UWB Networks

Ultra-Wide Band (UWB) is an emerging wireless physical layer technology that uses a very large bandwidth. We are interested in finding the design objectives of the medium access (MAC, namely, power control and scheduling) and routing protocols of a multi-hop, best-effort, UWB network. Our objective is to maximize flow rates (more precisely, log-utility of flow rates) given node power constraints. The specificity of UWB is expressed by the linear dependence between rate and signal-to-noise ratio at the receiver. It is known that, in wireless networks, different routing strategies can imply differences in MAC protocol design. Hence we search for the jointly optimal routing, scheduling and power control. We find that the optimal solution is characterized by the following. (1) When data is being sent over a link, it is optimal to have an exclusion region around the destination, in which all nodes remain silent during transmission, whereas nodes outside of this region can transmit in parallel, regardless of the interference they produce at the destination. Additionally, the source adapts its transmission rate according to the level of interference at the destination due to sources outside of the exclusion region. (2) The optimal size of this exclusion region depends only on the transmission power of the source of the link, and not on the length of the link nor on positions of nodes in its vicinity. (3) Each node in a given time slot either sends data at the maximum power, or does not send at all. As for the routing, we restrict ourselves to a subset of routes where on each successive hop we decrease the distance toward the destination, and we show that (4) relaying along a minimum energy and loss route is always better than using longer hops or sending directly, which is not obvious since we optimize rate and not power consumption. Finally (5), the design of the optimal MAC protocol is independent of the choice of the routing protocol. For narrow-band networks, (2), (4) and (5) do not hold, which shows that the design of an UWB network should be addressed in a different way than for narrow-band. Our technical approach is based on expressing the design requirements as a mathematical optimization problem. We solve it exactly for simple networks on a line and approximately on random topologies in a plane with up to 50 nodes with various power constraints, traffic matrices, and mobility parameters

When Power Adaptation is Useless or Harmful

We consider the design of optimal strategies for joint power adaptation, rate adaptation and scheduling in a multi-hop wireless network. Most existing strategies for ad-hoc networks control either power and scheduling, or rates and scheduling, but not the three together as we do. We assume the underlying physical layer allows fine-grained rate adaptation (like in 802.11a/g, HDR/CDMA, UWB). Our goal is to find properties of the power control in an optimal joint design. In the linear regime (i.e when the rate of a link can be approximated by a linear function of signal-to-noise ratio, SNR), we prove analytically that it is always optimal to use the simple 0-PMAX power control (when a node is sending it uses the maximum transmitting power allowed). This holds in both important networking scenarios: high rate networks where the goal is to maximize rates under power constraints, and low power networks where the goal is to minimize average consumed power while meeting minimum rate constraints. Moreover, we prove that, when maximizing rates, 0-PMAX is the only possible optimal power control strategy. Outside the linear regime, we do not know what the optimal power control is. We show that in the power minimization scenario, in some cases, rate adaptation and 0-PMAX power control performs much worse than power adaptation. Nevertheless, we conjecture, and we demonstrate numerically that when maximizing rates, even outside the linear regime, 0-PMAX is very close to the optimal power control, and the rate adaptation with 0-PMAX outperforms power adaptation with fixed link rates

A Joint PHY/MAC Architecture for Low-Radiated Power TH-UWB Wireless Ad-Hoc Networks

Due to environmental concerns and strict constraints on interference imposed on other networks, the radiated power of emerging pervasive wireless networks needs to be strictly limited, yet without sacrificing acceptable data rates. Pulsed Time-Hopping Ultra-Wide Band (TH-UWB) is a radio technology that has the potential to satisfy this requirement. Although TH-UWB is a multi-user radio technology, non-zero cross-correlation between time-hopping sequences, time-asynchronicity between sources and a multipath channel environment make it sensitive to strong interferers and near-far scenarios. While most protocols manage interference and multiple-access through power control or mutual exclusion (CSMA/CA or TDMA), we base our design on rate control, a relatively unexplored dimension for multiple-access and interference management. We further take advantage of the nature of pulsed TH-UWB to propose an interference mitigation scheme that reduces the impact of strong interferers. A source is always allowed to send and continuously adapts its channel code (hence its rate) to the interference experienced at the destination. In contrast to power control or exclusion, our MAC layer is local to sender and receiver and does not need coordination among neighbors not involved in the transmission. We show by simulation that we achieve a significant increase in network throughput

Bmi1 Is Expressed in Postnatal Myogenic Satellite Cells, Controls Their Maintenance and Plays an Essential Role in Repeated Muscle Regeneration

PMCID: PMC3212532This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited

Time Never Regained: Film, Memory and History in Mila Turajlić’s Labudović Reels

The article reviews the documentary film diptych The Labudović Reels by film-maker Mila Turajlić. Based on her archival work at the Filmske Novosti production company, Turajlić discovers the legacy of hitherto unknown cinematographer Stevan Labudović. Both films are hybrid documentaries that combine archive footage with interview-style documentary, and both focus on two intertwined thematic cycles––Labudović’s coverage of the Algerian war of independence (1959–1961) and the first Summit of the Non-Aligned Movement (1960–1961). Conceptually, Turajlić’s films engage thought-provoking matrixes, among them Pierre Nora’s lieux de memoire and, more especially, Walter Benjamin’s reflections on historical progress. This review finds that the implementation of the latter framework blurs the boundary between the critique of the idea of progress and historical relativism, which leads to the confusing presence of mutually exclusive voices in her film, one voice calling for the reappropriation of the past, and another calling that same past into question